Robert De Niro in Raging Bull (1980)
ROBERT DE NIRO:
#10: Jake La Motta in Raging Bull
#42: Travis Bickle in Taxi Driver
These are highly popular actors so the fans are more likely to vote for their personal favorite but the actual question is: which pair of performances from the same actor do you think is the best (and check the titles, they might surprise you).
(some bit of trivia: among the 28 performances, 6 were not Oscar-nominated, and out of the 22 Oscar-nominated ones, 6 won the Oscar)